How Do I Apply Stolz-Cesaro Theorem to Find the Limit of a Sequence?

[LazuRazvan]

Homework Statement

hello, i have to find the limit of the next array

(xn)=(cos (π/n+1) + cos (π/n+2) + ...+ cos ( π/2n))/n
when n goes to infinity.

Homework Equations

I was told to apply stolz cesaro and that is where i ended up :
the limit is :

limit of cos ( π/2n+1) + cos (π/2n+2) -cos (π/n+1)

The Attempt at a Solution

How i finish this ?

 

[Mark44]

Homework Statement

hello, i have to find the limit of the next array

(xn)=(cos (π/n+1) + cos (π/n+2) + ...+ cos ( π/2n))/n

What you wrote in the first term was $\cos(\frac{\pi}{n} + 1)$, and similar in the other two terms. Is that what you intended?

when n goes to infinity.

Homework Equations

I was told to apply stolz cesaro and that is where i ended up :
the limit is :

limit of cos ( π/2n+1) + cos (π/2n+2) -cos (π/n+1)

Same comment as above.

Also, to apply Stolz-Cesaro (https://en.wikipedia.org/wiki/Stolz–Cesàro_theorem), you need to use it with another sequence. What's the other sequence you are using?

The Attempt at a Solution

How i finish this ?